| | step type | requirements | statement |
| 0 | modus ponens | 1, 2 | ⊢  |
| 1 | instantiation | 3, 4*, 5*, 6* | ⊢  |
| | : , : , :  |
| 2 | instantiation | 7, 8, 9 | ⊢  |
| | : , :  |
| 3 | conjecture | | ⊢  |
| | proveit.numbers.number_sets.natural_numbers.fold_forall_natural_pos |
| 4 | instantiation | 603, 10, 450 | ⊢  |
| | : , : , :  |
| 5 | instantiation | 11, 12 | ⊢  |
| | :  |
| 6 | instantiation | 603, 13, 14 | ⊢  |
| | : , : , :  |
| 7 | theorem | | ⊢  |
| | proveit.logic.booleans.conjunction.and_if_both |
| 8 | instantiation | 428, 15, 16 | ⊢  |
| | : , : , :  |
| 9 | generalization | 17 | ⊢  |
| 10 | instantiation | 617, 632 | ⊢  |
| | : , : , :  |
| 11 | conjecture | | ⊢  |
| | proveit.physics.quantum.algebra.single_qubit_num_ket |
| 12 | instantiation | 18, 19, 20 | ⊢  |
| | :  |
| 13 | instantiation | 617, 126 | ⊢  |
| | : , : , :  |
| 14 | instantiation | 462, 21 | ⊢  |
| | : , :  |
| 15 | instantiation | 102, 681, 22, 23* | ⊢  |
| | :  |
| 16 | instantiation | 617, 24 | ⊢  |
| | : , : , :  |
| 17 | instantiation | 462, 25 | , ⊢  |
| | : , :  |
| 18 | conjecture | | ⊢  |
| | proveit.numbers.number_sets.integers.nonneg_int_is_natural |
| 19 | instantiation | 684, 26, 28 | ⊢  |
| | : , : , :  |
| 20 | instantiation | 27, 638, 665, 28 | ⊢  |
| | : , : , :  |
| 21 | instantiation | 29, 646, 681, 673, 632* | ⊢  |
| | : , : , :  |
| 22 | instantiation | 545, 30, 31 | ⊢  |
| | : , : , :  |
| 23 | instantiation | 603, 32, 33 | ⊢  |
| | : , : , :  |
| 24 | instantiation | 34, 638, 665, 35, 36*, 37* | ⊢  |
| | : , : , : , :  |
| 25 | instantiation | 545, 38, 39 | , ⊢  |
| | : , : , :  |
| 26 | instantiation | 637, 638, 665 | ⊢  |
| | : , :  |
| 27 | conjecture | | ⊢  |
| | proveit.numbers.number_sets.integers.interval_lower_bound |
| 28 | assumption | | ⊢  |
| 29 | conjecture | | ⊢  |
| | proveit.numbers.exponentiation.product_of_posnat_powers |
| 30 | instantiation | 479, 345, 615, 298 | ⊢  |
| | : , : , :  |
| 31 | instantiation | 494, 615, 577 | ⊢  |
| | : , :  |
| 32 | instantiation | 617, 40 | ⊢  |
| | : , : , :  |
| 33 | instantiation | 41, 487, 42 | ⊢  |
| | : , : , :  |
| 34 | conjecture | | ⊢  |
| | proveit.linear_algebra.addition.vec_sum_split_first |
| 35 | conjecture | | ⊢  |
| | proveit.numbers.numerals.decimals.less_0_1 |
| 36 | instantiation | 603, 43, 44 | ⊢  |
| | : , : , :  |
| 37 | instantiation | 603, 45, 46 | ⊢  |
| | : , : , :  |
| 38 | instantiation | 545, 47, 48, 49* | , ⊢  |
| | : , : , :  |
| 39 | instantiation | 603, 50, 51 | ⊢  |
| | : , : , :  |
| 40 | instantiation | 52, 681, 53 | ⊢  |
| | : , : , :  |
| 41 | axiom | | ⊢  |
| | proveit.linear_algebra.tensors.unary_tensor_prod_def |
| 42 | instantiation | 455, 487, 203, 54 | ⊢  |
| | : , : , : , :  |
| 43 | instantiation | 617, 55 | ⊢  |
| | : , : , :  |
| 44 | instantiation | 56, 615, 324, 487 | ⊢  |
| | : , : , :  |
| 45 | instantiation | 617, 57 | ⊢  |
| | : , : , :  |
| 46 | instantiation | 58, 665, 59* | ⊢  |
| | : , :  |
| 47 | instantiation | 428, 60, 61 | , ⊢  |
| | : , : , :  |
| 48 | instantiation | 102, 673 | ⊢  |
| | :  |
| 49 | instantiation | 603, 62, 63 | ⊢  |
| | : , : , :  |
| 50 | instantiation | 462, 64 | ⊢  |
| | : , :  |
| 51 | instantiation | 462, 65 | ⊢  |
| | : , :  |
| 52 | conjecture | | ⊢  |
| | proveit.core_expr_types.tuples.tuple_eq_via_elem_eq |
| 53 | instantiation | 617, 66 | ⊢  |
| | : , : , :  |
| 54 | instantiation | 323, 487, 324, 67 | ⊢  |
| | : , : , : , :  |
| 55 | instantiation | 603, 68, 69 | ⊢  |
| | : , : , :  |
| 56 | conjecture | | ⊢  |
| | proveit.linear_algebra.scalar_multiplication.one_as_scalar_mult_id |
| 57 | modus ponens | 70, 71 | ⊢  |
| 58 | axiom | | ⊢  |
| | proveit.linear_algebra.addition.vec_sum_single |
| 59 | instantiation | 593, 422, 612, 423, 614, 646, 569, 582, 583 | ⊢  |
| | : , : , : , :  |
| 60 | instantiation | 545, 72, 73 | ⊢  |
| | : , : , :  |
| 61 | assumption | | ⊢  |
| 62 | instantiation | 74, 674, 194, 612, 164, 106, 614, 487, 107, 108, 75, 110 | ⊢  |
| | : , : , : , : , : , : , : , : , : , :  |
| 63 | instantiation | 458, 281, 612, 194, 614, 164, 106, 487, 107, 108, 278, 110 | ⊢  |
| | : , : , : , : , : , : , : , : , : , :  |
| 64 | instantiation | 76, 686, 77, 78, 79, 80 | ⊢  |
| | : , : , : , :  |
| 65 | instantiation | 81, 158, 82, 83, 84, 85, 86* | ⊢  |
| | : , : , : , :  |
| 66 | instantiation | 617, 87 | ⊢  |
| | : , : , :  |
| 67 | instantiation | 455, 487, 88, 490 | ⊢  |
| | : , : , : , :  |
| 68 | instantiation | 617, 89 | ⊢  |
| | : , : , :  |
| 69 | instantiation | 301, 492 | ⊢  |
| | :  |
| 70 | instantiation | 90, 681 | ⊢  |
| | : , : , : , : , : , :  |
| 71 | generalization | 91 | ⊢  |
| 72 | instantiation | 92, 93 | ⊢  |
| | : , : , :  |
| 73 | instantiation | 603, 94, 95 | ⊢  |
| | : , : , :  |
| 74 | conjecture | | ⊢  |
| | proveit.linear_algebra.tensors.tensor_prod_disassociation |
| 75 | instantiation | 455, 487, 281, 278 | ⊢  |
| | : , : , : , :  |
| 76 | axiom | | ⊢  |
| | proveit.core_expr_types.operations.operands_substitution |
| 77 | instantiation | 626 | ⊢  |
| | : , :  |
| 78 | instantiation | 626 | ⊢  |
| | : , :  |
| 79 | instantiation | 462, 438 | ⊢  |
| | : , :  |
| 80 | instantiation | 617, 96 | ⊢  |
| | : , : , :  |
| 81 | conjecture | | ⊢  |
| | proveit.logic.equality.sub_in_right_operands_via_tuple |
| 82 | instantiation | 283, 97, 98, 101 | ⊢  |
| | : , : , : , :  |
| 83 | instantiation | 283, 99, 100, 101 | ⊢  |
| | : , : , : , :  |
| 84 | instantiation | 102, 640, 103 | ⊢  |
| | :  |
| 85 | instantiation | 104, 105, 292* | ⊢  |
| | : , : , :  |
| 86 | instantiation | 458, 203, 612, 194, 614, 164, 106, 487, 107, 108, 109, 110 | ⊢  |
| | : , : , : , : , : , : , : , : , : , :  |
| 87 | instantiation | 617, 111 | ⊢  |
| | : , : , :  |
| 88 | instantiation | 542, 492, 112 | ⊢  |
| | : , :  |
| 89 | instantiation | 113, 422, 612, 423, 614, 646, 569, 582, 583 | ⊢  |
| | : , : , : , :  |
| 90 | axiom | | ⊢  |
| | proveit.core_expr_types.lambda_maps.lambda_substitution |
| 91 | instantiation | 617, 114 | ⊢  |
| | : , : , :  |
| 92 | theorem | | ⊢  |
| | proveit.linear_algebra.scalar_multiplication.scalar_mult_eq |
| 93 | instantiation | 142, 115, 116 | ⊢  |
| | : , :  |
| 94 | instantiation | 617, 117 | ⊢  |
| | : , : , :  |
| 95 | instantiation | 462, 118 | ⊢  |
| | : , :  |
| 96 | instantiation | 462, 135 | ⊢  |
| | : , :  |
| 97 | instantiation | 545, 119, 120 | ⊢  |
| | : , : , :  |
| 98 | instantiation | 574 | ⊢  |
| | :  |
| 99 | instantiation | 121, 683, 122, 123, 124, 125, 194, 157*, 164* | ⊢  |
| | : , : , : , :  |
| 100 | instantiation | 462, 126 | ⊢  |
| | : , :  |
| 101 | instantiation | 462, 127 | ⊢  |
| | : , :  |
| 102 | axiom | | ⊢  |
| | proveit.physics.quantum.QPE._psi_t_def |
| 103 | instantiation | 603, 128, 129 | ⊢  |
| | : , : , :  |
| 104 | conjecture | | ⊢  |
| | proveit.core_expr_types.tuples.partition_front |
| 105 | instantiation | 130, 612, 191 | ⊢  |
| | : , :  |
| 106 | instantiation | 283, 131, 411, 134 | ⊢  |
| | : , : , : , :  |
| 107 | instantiation | 132, 622, 638, 487, 168 | ⊢  |
| | : , : , :  |
| 108 | instantiation | 283, 133, 411, 134 | ⊢  |
| | : , : , : , :  |
| 109 | instantiation | 545, 278, 135 | ⊢  |
| | : , : , :  |
| 110 | modus ponens | 136, 137 | ⊢  |
| 111 | instantiation | 617, 138 | ⊢  |
| | : , : , :  |
| 112 | instantiation | 545, 139, 140 | ⊢  |
| | : , : , :  |
| 113 | conjecture | | ⊢  |
| | proveit.numbers.multiplication.mult_zero_any |
| 114 | instantiation | 617, 141 | ⊢  |
| | : , : , :  |
| 115 | instantiation | 142, 143, 144 | ⊢  |
| | : , :  |
| 116 | instantiation | 617, 145, 146*, 147*, 148* | ⊢  |
| | : , : , :  |
| 117 | instantiation | 603, 149, 150 | ⊢  |
| | : , : , :  |
| 118 | instantiation | 283, 151, 152, 153 | ⊢  |
| | : , : , : , :  |
| 119 | instantiation | 193, 154 | ⊢  |
| | : , : , :  |
| 120 | instantiation | 603, 155, 156 | ⊢  |
| | : , : , :  |
| 121 | conjecture | | ⊢  |
| | proveit.core_expr_types.tuples.general_len |
| 122 | instantiation | 626 | ⊢  |
| | : , :  |
| 123 | instantiation | 626 | ⊢  |
| | : , :  |
| 124 | instantiation | 626 | ⊢  |
| | : , :  |
| 125 | instantiation | 428, 674, 157 | ⊢  |
| | : , : , :  |
| 126 | instantiation | 494, 620, 615 | ⊢  |
| | : , :  |
| 127 | instantiation | 197, 158 | ⊢  |
| | : , :  |
| 128 | instantiation | 617, 159 | ⊢  |
| | : , : , :  |
| 129 | instantiation | 603, 160, 161 | ⊢  |
| | : , : , :  |
| 130 | conjecture | | ⊢  |
| | proveit.numbers.addition.add_nat_closure_bin |
| 131 | instantiation | 545, 162, 164 | ⊢  |
| | : , : , :  |
| 132 | conjecture | | ⊢  |
| | proveit.logic.booleans.conjunction.redundant_conjunction_general |
| 133 | instantiation | 545, 163, 164 | ⊢  |
| | : , : , :  |
| 134 | instantiation | 462, 165 | ⊢  |
| | : , :  |
| 135 | instantiation | 617, 166 | ⊢  |
| | : , : , :  |
| 136 | instantiation | 167, 622, 638, 168 | ⊢  |
| | : , : , : , :  |
| 137 | generalization | 169 | ⊢  |
| 138 | instantiation | 603, 170, 171 | ⊢  |
| | : , : , :  |
| 139 | instantiation | 581, 548, 566 | ⊢  |
| | : , :  |
| 140 | instantiation | 603, 172, 173 | ⊢  |
| | : , : , :  |
| 141 | instantiation | 617, 298 | ⊢  |
| | : , : , :  |
| 142 | theorem | | ⊢  |
| | proveit.logic.equality.rhs_via_equality |
| 143 | instantiation | 545, 174, 175 | ⊢  |
| | : , : , :  |
| 144 | instantiation | 617, 176, 177*, 178*, 179* | ⊢  |
| | : , : , :  |
| 145 | modus ponens | 180, 181 | ⊢  |
| 146 | instantiation | 317, 624 | ⊢  |
| | : , :  |
| 147 | instantiation | 317, 624 | ⊢  |
| | : , :  |
| 148 | instantiation | 462, 182 | ⊢  |
| | : , :  |
| 149 | instantiation | 617, 183 | ⊢  |
| | : , : , :  |
| 150 | modus ponens | 184, 185 | ⊢  |
| 151 | instantiation | 603, 186, 187, 188* | ⊢  |
| | : , : , :  |
| 152 | instantiation | 617, 189 | ⊢  |
| | : , : , :  |
| 153 | instantiation | 574 | ⊢  |
| | :  |
| 154 | instantiation | 235, 549, 190, 612, 191, 674 | ⊢  |
| | : , :  |
| 155 | instantiation | 617, 292 | ⊢  |
| | : , : , :  |
| 156 | instantiation | 346, 612, 686, 614, 613, 620, 615 | ⊢  |
| | : , : , : , :  |
| 157 | instantiation | 342, 615, 309 | ⊢  |
| | : , : , :  |
| 158 | instantiation | 684, 672, 640 | ⊢  |
| | : , : , :  |
| 159 | instantiation | 291, 620, 615 | ⊢  |
| | : , :  |
| 160 | instantiation | 554, 612, 686, 674, 614, 192, 409, 577, 615 | ⊢  |
| | : , : , : , : , : , :  |
| 161 | instantiation | 308, 615, 409, 309 | ⊢  |
| | : , : , :  |
| 162 | instantiation | 193, 194 | ⊢  |
| | : , : , :  |
| 163 | instantiation | 193, 194 | ⊢  |
| | : , : , :  |
| 164 | instantiation | 603, 195, 196 | ⊢  |
| | : , : , :  |
| 165 | instantiation | 197, 663 | ⊢  |
| | : , :  |
| 166 | instantiation | 462, 198 | ⊢  |
| | : , :  |
| 167 | conjecture | | ⊢  |
| | proveit.logic.booleans.conjunction.conjunction_from_quantification |
| 168 | instantiation | 375, 199, 257, 633, 200, 201*, 202* | ⊢  |
| | : , : , :  |
| 169 | instantiation | 455, 487, 203, 204 | , ⊢  |
| | : , : , : , :  |
| 170 | instantiation | 617, 205 | ⊢  |
| | : , : , :  |
| 171 | instantiation | 593, 549, 674, 340, 646, 569, 582, 583 | ⊢  |
| | : , : , : , :  |
| 172 | instantiation | 576, 674, 686, 612, 567, 614, 548, 582, 583 | ⊢  |
| | : , : , : , : , : , :  |
| 173 | instantiation | 576, 612, 686, 614, 550, 567, 646, 569, 582, 583 | ⊢  |
| | : , : , : , : , : , :  |
| 174 | instantiation | 206, 638, 639, 211, 207, 208, 209* | ⊢  |
| | : , : , : , : , :  |
| 175 | instantiation | 210, 651, 211, 447, 212*, 213*, 214* | ⊢  |
| | : , : , : , : , :  |
| 176 | modus ponens | 215, 216 | ⊢  |
| 177 | instantiation | 317, 624 | ⊢  |
| | : , :  |
| 178 | instantiation | 317, 624 | ⊢  |
| | : , :  |
| 179 | instantiation | 283, 217, 218, 219 | ⊢  |
| | : , : , : , :  |
| 180 | instantiation | 360, 681 | ⊢  |
| | : , : , : , : , : , : , :  |
| 181 | generalization | 220 | ⊢  |
| 182 | modus ponens | 221, 222 | ⊢  |
| 183 | instantiation | 462, 223 | ⊢  |
| | : , :  |
| 184 | instantiation | 224, 612, 686, 674, 225, 614, 226 | ⊢  |
| | : , : , : , : , : , : , : , :  |
| 185 | instantiation | 647, 227, 231 | ⊢  |
| | : , : , :  |
| 186 | instantiation | 458, 281, 612, 674, 614, 487, 488, 278, 228 | ⊢  |
| | : , : , : , : , : , : , : , : , : , :  |
| 187 | instantiation | 617, 229 | ⊢  |
| | : , : , :  |
| 188 | instantiation | 230, 456, 231, 281, 282, 232* | ⊢  |
| | : , : , : , : , :  |
| 189 | instantiation | 462, 233 | ⊢  |
| | : , :  |
| 190 | instantiation | 570 | ⊢  |
| | : , : , :  |
| 191 | instantiation | 684, 672, 234 | ⊢  |
| | : , : , :  |
| 192 | instantiation | 626 | ⊢  |
| | : , :  |
| 193 | conjecture | | ⊢  |
| | proveit.core_expr_types.tuples.range_len |
| 194 | instantiation | 235, 549, 236, 612, 237, 674 | ⊢  |
| | : , :  |
| 195 | instantiation | 617, 238 | ⊢  |
| | : , : , :  |
| 196 | instantiation | 283, 239, 240, 241 | ⊢  |
| | : , : , : , :  |
| 197 | conjecture | | ⊢  |
| | proveit.core_expr_types.tuples.range_from1_len |
| 198 | instantiation | 617, 242 | ⊢  |
| | : , : , :  |
| 199 | instantiation | 684, 670, 243 | ⊢  |
| | : , : , :  |
| 200 | instantiation | 244, 245 | ⊢  |
| | : , :  |
| 201 | instantiation | 603, 246, 247 | ⊢  |
| | : , : , :  |
| 202 | instantiation | 283, 248, 309, 249 | ⊢  |
| | : , : , : , :  |
| 203 | instantiation | 460, 615, 467, 468 | ⊢  |
| | : , :  |
| 204 | instantiation | 323, 487, 324, 250 | , ⊢  |
| | : , : , : , :  |
| 205 | instantiation | 603, 251, 252 | ⊢  |
| | : , : , :  |
| 206 | conjecture | | ⊢  |
| | proveit.linear_algebra.addition.vec_sum_split_after |
| 207 | instantiation | 253, 254 | ⊢  |
| | : , :  |
| 208 | instantiation | 255, 256, 257, 544, 258, 259*, 260* | ⊢  |
| | : , : , :  |
| 209 | instantiation | 603, 261, 262 | ⊢  |
| | : , : , :  |
| 210 | conjecture | | ⊢  |
| | proveit.linear_algebra.addition.vec_sum_index_shift |
| 211 | instantiation | 650, 446, 652 | ⊢  |
| | : , :  |
| 212 | instantiation | 410, 527, 263 | ⊢  |
| | : , :  |
| 213 | instantiation | 603, 264, 265 | ⊢  |
| | : , : , :  |
| 214 | instantiation | 338, 527 | ⊢  |
| | :  |
| 215 | instantiation | 360, 681 | ⊢  |
| | : , : , : , : , : , : , :  |
| 216 | generalization | 266 | ⊢  |
| 217 | instantiation | 617, 267, 268*, 269* | ⊢  |
| | : , : , :  |
| 218 | instantiation | 462, 270 | ⊢  |
| | : , :  |
| 219 | instantiation | 617, 271 | ⊢  |
| | : , : , :  |
| 220 | instantiation | 272, 673, 624 | , ⊢  |
| | : , :  |
| 221 | instantiation | 393, 674, 681, 612, 456, 614 | ⊢  |
| | : , : , : , : , : , : , : , : , : , : , :  |
| 222 | generalization | 273 | ⊢  |
| 223 | instantiation | 458, 391, 612, 674, 614, 487, 488, 490, 279 | ⊢  |
| | : , : , : , : , : , : , : , : , : , :  |
| 224 | conjecture | | ⊢  |
| | proveit.linear_algebra.tensors.tensor_prod_factorization_from_add |
| 225 | instantiation | 511, 274 | ⊢  |
| | :  |
| 226 | instantiation | 626 | ⊢  |
| | : , :  |
| 227 | instantiation | 275, 683, 276, 512 | ⊢  |
| | : , : , :  |
| 228 | instantiation | 455, 488, 282, 279 | ⊢  |
| | : , : , : , :  |
| 229 | instantiation | 458, 282, 674, 612, 614, 487, 488, 278, 279 | ⊢  |
| | : , : , : , : , : , : , : , : , : , :  |
| 230 | conjecture | | ⊢  |
| | proveit.linear_algebra.scalar_multiplication.doubly_scaled_as_singly_scaled |
| 231 | instantiation | 485, 683, 486, 487, 488, 277, 278, 279 | ⊢  |
| | : , : , : , :  |
| 232 | instantiation | 280, 281, 282 | ⊢  |
| | : , :  |
| 233 | instantiation | 283, 284, 285, 286 | ⊢  |
| | : , : , : , :  |
| 234 | instantiation | 287, 288 | ⊢  |
| | :  |
| 235 | conjecture | | ⊢  |
| | proveit.numbers.addition.add_nat_closure |
| 236 | instantiation | 570 | ⊢  |
| | : , : , :  |
| 237 | instantiation | 289, 290 | ⊢  |
| | :  |
| 238 | instantiation | 291, 409, 615, 292* | ⊢  |
| | : , :  |
| 239 | instantiation | 554, 674, 686, 293, 345, 620, 577, 615 | ⊢  |
| | : , : , : , : , : , :  |
| 240 | instantiation | 346, 612, 549, 614, 294, 620, 577, 615 | ⊢  |
| | : , : , : , :  |
| 241 | instantiation | 308, 615, 620, 309 | ⊢  |
| | : , : , :  |
| 242 | instantiation | 617, 295 | ⊢  |
| | : , : , :  |
| 243 | instantiation | 684, 679, 622 | ⊢  |
| | : , : , :  |
| 244 | conjecture | | ⊢  |
| | proveit.numbers.ordering.relax_less |
| 245 | instantiation | 303, 673 | ⊢  |
| | :  |
| 246 | instantiation | 554, 674, 686, 612, 341, 614, 345, 409, 615 | ⊢  |
| | : , : , : , : , : , :  |
| 247 | instantiation | 346, 612, 686, 614, 341, 409, 615 | ⊢  |
| | : , : , : , :  |
| 248 | instantiation | 603, 296, 297 | ⊢  |
| | : , : , :  |
| 249 | instantiation | 462, 298 | ⊢  |
| | : , :  |
| 250 | instantiation | 455, 487, 299, 490 | , ⊢  |
| | : , : , : , :  |
| 251 | instantiation | 617, 300 | ⊢  |
| | : , : , :  |
| 252 | instantiation | 301, 646 | ⊢  |
| | :  |
| 253 | conjecture | | ⊢  |
| | proveit.numbers.addition.subtraction.nonneg_difference |
| 254 | instantiation | 408, 512 | ⊢  |
| | :  |
| 255 | conjecture | | ⊢  |
| | proveit.numbers.addition.strong_bound_via_left_term_bound |
| 256 | instantiation | 684, 670, 302 | ⊢  |
| | : , : , :  |
| 257 | conjecture | | ⊢  |
| | proveit.numbers.number_sets.real_numbers.zero_is_real |
| 258 | instantiation | 303, 512 | ⊢  |
| | :  |
| 259 | instantiation | 603, 304, 305 | ⊢  |
| | : , : , :  |
| 260 | instantiation | 603, 306, 307 | ⊢  |
| | : , : , :  |
| 261 | instantiation | 554, 612, 686, 674, 614, 347, 527, 577, 615 | ⊢  |
| | : , : , : , : , : , :  |
| 262 | instantiation | 308, 615, 527, 309 | ⊢  |
| | : , : , :  |
| 263 | instantiation | 574 | ⊢  |
| | :  |
| 264 | instantiation | 554, 612, 686, 674, 614, 310, 353, 577, 354 | ⊢  |
| | : , : , : , : , : , :  |
| 265 | instantiation | 603, 311, 312 | ⊢  |
| | : , : , :  |
| 266 | instantiation | 545, 313, 314 | , ⊢  |
| | : , : , :  |
| 267 | modus ponens | 315, 316 | ⊢  |
| 268 | instantiation | 317, 624 | ⊢  |
| | : , :  |
| 269 | instantiation | 317, 624 | ⊢  |
| | : , :  |
| 270 | modus ponens | 318, 319 | ⊢  |
| 271 | instantiation | 462, 320 | ⊢  |
| | : , :  |
| 272 | conjecture | | ⊢  |
| | proveit.physics.quantum.algebra.prepend_num_ket_with_zero_ket |
| 273 | instantiation | 485, 683, 486, 487, 488, 321, 324, 367 | , ⊢  |
| | : , : , : , :  |
| 274 | instantiation | 322, 683, 512 | ⊢  |
| | : , :  |
| 275 | conjecture | | ⊢  |
| | proveit.linear_algebra.tensors.tensor_prod_of_cart_exps_within_cart_exp |
| 276 | instantiation | 626 | ⊢  |
| | : , :  |
| 277 | instantiation | 626 | ⊢  |
| | : , :  |
| 278 | instantiation | 323, 487, 324, 325 | ⊢  |
| | : , : , : , :  |
| 279 | modus ponens | 326, 327 | ⊢  |
| 280 | axiom | | ⊢  |
| | proveit.linear_algebra.scalar_multiplication.scalar_mult_extends_number_mult |
| 281 | instantiation | 460, 615, 328, 329 | ⊢  |
| | : , :  |
| 282 | instantiation | 460, 615, 330, 331 | ⊢  |
| | : , :  |
| 283 | conjecture | | ⊢  |
| | proveit.logic.equality.four_chain_transitivity |
| 284 | instantiation | 603, 332, 333 | ⊢  |
| | : , : , :  |
| 285 | instantiation | 574 | ⊢  |
| | :  |
| 286 | instantiation | 462, 334 | ⊢  |
| | : , :  |
| 287 | conjecture | | ⊢  |
| | proveit.numbers.negation.nat_pos_closure |
| 288 | instantiation | 335, 673 | ⊢  |
| | :  |
| 289 | conjecture | | ⊢  |
| | proveit.numbers.negation.nat_closure |
| 290 | instantiation | 336, 622, 337 | ⊢  |
| | :  |
| 291 | conjecture | | ⊢  |
| | proveit.numbers.negation.distribute_neg_through_binary_sum |
| 292 | instantiation | 338, 620 | ⊢  |
| | :  |
| 293 | instantiation | 626 | ⊢  |
| | : , :  |
| 294 | instantiation | 570 | ⊢  |
| | : , : , :  |
| 295 | instantiation | 339, 549, 674, 612, 340, 614, 646, 569, 582, 527, 583 | ⊢  |
| | : , : , : , : , : , : , :  |
| 296 | instantiation | 554, 674, 686, 612, 341, 614, 620, 409, 615 | ⊢  |
| | : , : , : , : , : , :  |
| 297 | instantiation | 342, 620, 615, 411 | ⊢  |
| | : , : , :  |
| 298 | instantiation | 343, 615 | ⊢  |
| | :  |
| 299 | instantiation | 542, 492, 344 | , ⊢  |
| | : , :  |
| 300 | conjecture | | ⊢  |
| | proveit.numbers.negation.negated_zero |
| 301 | conjecture | | ⊢  |
| | proveit.numbers.exponentiation.exp_zero_eq_one |
| 302 | instantiation | 684, 679, 639 | ⊢  |
| | : , : , :  |
| 303 | conjecture | | ⊢  |
| | proveit.numbers.number_sets.natural_numbers.natural_pos_is_pos |
| 304 | instantiation | 554, 674, 686, 612, 347, 614, 345, 527, 577 | ⊢  |
| | : , : , : , : , : , :  |
| 305 | instantiation | 346, 612, 686, 614, 347, 527, 577 | ⊢  |
| | : , : , : , :  |
| 306 | instantiation | 554, 674, 686, 612, 347, 614, 527, 577 | ⊢  |
| | : , : , : , : , : , :  |
| 307 | instantiation | 351, 612, 686, 674, 614, 348, 527, 577, 349* | ⊢  |
| | : , : , : , : , : , :  |
| 308 | conjecture | | ⊢  |
| | proveit.numbers.addition.subtraction.add_cancel_triple_32 |
| 309 | instantiation | 574 | ⊢  |
| | :  |
| 310 | instantiation | 626 | ⊢  |
| | : , :  |
| 311 | instantiation | 350, 674, 612, 614, 353, 577, 354 | ⊢  |
| | : , : , : , : , : , : , :  |
| 312 | instantiation | 351, 612, 686, 674, 614, 352, 353, 354, 577, 355* | ⊢  |
| | : , : , : , : , : , :  |
| 313 | instantiation | 428, 356, 357 | , ⊢  |
| | : , : , :  |
| 314 | instantiation | 603, 358, 359 | , ⊢  |
| | : , : , :  |
| 315 | instantiation | 360, 681 | ⊢  |
| | : , : , : , : , : , : , :  |
| 316 | generalization | 361 | ⊢  |
| 317 | conjecture | | ⊢  |
| | proveit.core_expr_types.conditionals.satisfied_condition_reduction |
| 318 | instantiation | 362, 681, 456, 391 | ⊢  |
| | : , : , : , : , : , : , : , :  |
| 319 | modus ponens | 363, 364 | ⊢  |
| 320 | modus ponens | 365, 366 | ⊢  |
| 321 | instantiation | 626 | ⊢  |
| | : , :  |
| 322 | conjecture | | ⊢  |
| | proveit.numbers.multiplication.mult_nat_pos_closure_bin |
| 323 | conjecture | | ⊢  |
| | proveit.linear_algebra.addition.binary_closure |
| 324 | conjecture | | ⊢  |
| | proveit.physics.quantum.algebra.ket_zero_in_qubit_space |
| 325 | instantiation | 455, 487, 391, 490 | ⊢  |
| | : , : , : , :  |
| 326 | instantiation | 392, 681, 488 | ⊢  |
| | : , : , : , : , : , :  |
| 327 | generalization | 367 | ⊢  |
| 328 | instantiation | 542, 646, 368 | ⊢  |
| | : , :  |
| 329 | instantiation | 428, 468, 466 | ⊢  |
| | : , : , :  |
| 330 | instantiation | 542, 646, 431 | ⊢  |
| | : , :  |
| 331 | instantiation | 428, 472, 470 | ⊢  |
| | : , : , :  |
| 332 | instantiation | 617, 369 | ⊢  |
| | : , : , :  |
| 333 | instantiation | 588, 615, 370, 371, 372* | ⊢  |
| | : , :  |
| 334 | instantiation | 603, 373, 374 | ⊢  |
| | : , : , :  |
| 335 | conjecture | | ⊢  |
| | proveit.numbers.negation.int_neg_closure |
| 336 | conjecture | | ⊢  |
| | proveit.numbers.number_sets.integers.nonpos_int_is_int_nonpos |
| 337 | instantiation | 375, 442, 627, 633, 376, 377*, 378* | ⊢  |
| | : , : , :  |
| 338 | conjecture | | ⊢  |
| | proveit.numbers.negation.double_negation |
| 339 | conjecture | | ⊢  |
| | proveit.numbers.multiplication.leftward_commutation |
| 340 | instantiation | 570 | ⊢  |
| | : , : , :  |
| 341 | instantiation | 626 | ⊢  |
| | : , :  |
| 342 | conjecture | | ⊢  |
| | proveit.numbers.addition.subtraction.add_cancel_triple_12 |
| 343 | conjecture | | ⊢  |
| | proveit.numbers.addition.elim_zero_left |
| 344 | instantiation | 545, 379, 380 | , ⊢  |
| | : , : , :  |
| 345 | conjecture | | ⊢  |
| | proveit.numbers.number_sets.complex_numbers.zero_is_complex |
| 346 | conjecture | | ⊢  |
| | proveit.numbers.addition.elim_zero_any |
| 347 | instantiation | 626 | ⊢  |
| | : , :  |
| 348 | instantiation | 626 | ⊢  |
| | : , :  |
| 349 | instantiation | 462, 381, 480* | ⊢  |
| | : , :  |
| 350 | conjecture | | ⊢  |
| | proveit.numbers.addition.leftward_commutation |
| 351 | conjecture | | ⊢  |
| | proveit.numbers.addition.association |
| 352 | instantiation | 626 | ⊢  |
| | : , :  |
| 353 | instantiation | 684, 657, 382 | ⊢  |
| | : , : , :  |
| 354 | instantiation | 684, 657, 383 | ⊢  |
| | : , : , :  |
| 355 | instantiation | 603, 384, 385, 386* | ⊢  |
| | : , : , :  |
| 356 | instantiation | 617, 387 | , ⊢  |
| | : , : , :  |
| 357 | instantiation | 388, 529, 493, 427 | , ⊢  |
| | : , : , :  |
| 358 | instantiation | 462, 389 | , ⊢  |
| | : , :  |
| 359 | instantiation | 390, 673, 624 | , ⊢  |
| | : , :  |
| 360 | conjecture | | ⊢  |
| | proveit.core_expr_types.lambda_maps.general_lambda_substitution |
| 361 | instantiation | 619, 459, 391 | , ⊢  |
| | : , :  |
| 362 | conjecture | | ⊢  |
| | proveit.linear_algebra.scalar_multiplication.distribution_over_vec_sum_with_scalar_mult |
| 363 | instantiation | 392, 681, 456 | ⊢  |
| | : , : , : , : , : , :  |
| 364 | generalization | 429 | ⊢  |
| 365 | instantiation | 393, 674, 681, 612, 456, 614 | ⊢  |
| | : , : , : , : , : , : , : , : , : , : , :  |
| 366 | generalization | 394 | ⊢  |
| 367 | instantiation | 455, 488, 459, 491 | , ⊢  |
| | : , : , : , :  |
| 368 | instantiation | 395, 396, 397 | ⊢  |
| | : , :  |
| 369 | instantiation | 603, 398, 399 | ⊢  |
| | : , : , :  |
| 370 | instantiation | 581, 467, 471 | ⊢  |
| | : , :  |
| 371 | instantiation | 400, 686, 401, 402, 403 | ⊢  |
| | : , :  |
| 372 | instantiation | 603, 404, 405 | ⊢  |
| | : , : , :  |
| 373 | instantiation | 617, 406 | ⊢  |
| | : , : , :  |
| 374 | instantiation | 617, 407 | ⊢  |
| | : , : , :  |
| 375 | conjecture | | ⊢  |
| | proveit.numbers.addition.weak_bound_via_left_term_bound |
| 376 | instantiation | 408, 673 | ⊢  |
| | :  |
| 377 | instantiation | 494, 615, 409 | ⊢  |
| | : , :  |
| 378 | instantiation | 410, 620, 411 | ⊢  |
| | : , :  |
| 379 | instantiation | 581, 548, 412 | , ⊢  |
| | : , :  |
| 380 | instantiation | 603, 413, 414 | , ⊢  |
| | : , : , :  |
| 381 | instantiation | 611, 612, 686, 674, 614, 415, 615, 527, 421* | ⊢  |
| | : , : , : , : , : , :  |
| 382 | instantiation | 684, 670, 416 | ⊢  |
| | : , : , :  |
| 383 | instantiation | 684, 670, 417 | ⊢  |
| | : , : , :  |
| 384 | instantiation | 617, 418 | ⊢  |
| | : , : , :  |
| 385 | instantiation | 462, 419 | ⊢  |
| | : , :  |
| 386 | instantiation | 603, 420, 421 | ⊢  |
| | : , : , :  |
| 387 | instantiation | 611, 422, 686, 612, 423, 424, 614, 646, 569, 582, 583, 568, 527 | , ⊢  |
| | : , : , : , : , : , :  |
| 388 | conjecture | | ⊢  |
| | proveit.numbers.exponentiation.product_of_complex_powers |
| 389 | instantiation | 425, 426 | , ⊢  |
| | : , : , :  |
| 390 | conjecture | | ⊢  |
| | proveit.physics.quantum.algebra.prepend_num_ket_with_one_ket |
| 391 | instantiation | 542, 492, 427 | ⊢  |
| | : , :  |
| 392 | conjecture | | ⊢  |
| | proveit.linear_algebra.addition.summation_closure |
| 393 | conjecture | | ⊢  |
| | proveit.linear_algebra.tensors.tensor_prod_distribution_over_summation_with_scalar_mult |
| 394 | instantiation | 428, 429, 430 | , ⊢  |
| | : , : , :  |
| 395 | conjecture | | ⊢  |
| | proveit.numbers.addition.add_complex_closure_bin |
| 396 | instantiation | 460, 610, 646, 589 | ⊢  |
| | : , :  |
| 397 | instantiation | 592, 431 | ⊢  |
| | :  |
| 398 | instantiation | 617, 552 | ⊢  |
| | : , : , :  |
| 399 | instantiation | 603, 432, 433 | ⊢  |
| | : , : , :  |
| 400 | conjecture | | ⊢  |
| | proveit.numbers.multiplication.mult_not_eq_zero |
| 401 | instantiation | 626 | ⊢  |
| | : , :  |
| 402 | instantiation | 434, 467, 468 | ⊢  |
| | :  |
| 403 | instantiation | 434, 471, 472 | ⊢  |
| | :  |
| 404 | instantiation | 617, 435 | ⊢  |
| | : , : , :  |
| 405 | instantiation | 603, 436, 437 | ⊢  |
| | : , : , :  |
| 406 | instantiation | 603, 438, 439 | ⊢  |
| | : , : , :  |
| 407 | instantiation | 603, 440, 441 | ⊢  |
| | : , : , :  |
| 408 | conjecture | | ⊢  |
| | proveit.numbers.number_sets.natural_numbers.natural_pos_lower_bound |
| 409 | instantiation | 684, 657, 442 | ⊢  |
| | : , : , :  |
| 410 | conjecture | | ⊢  |
| | proveit.numbers.addition.subtraction.add_cancel_basic |
| 411 | instantiation | 574 | ⊢  |
| | :  |
| 412 | instantiation | 545, 443, 444 | , ⊢  |
| | : , : , :  |
| 413 | instantiation | 576, 674, 549, 612, 445, 614, 548, 582, 507, 583 | , ⊢  |
| | : , : , : , : , : , :  |
| 414 | instantiation | 576, 612, 686, 549, 614, 550, 445, 646, 569, 582, 507, 583 | , ⊢  |
| | : , : , : , : , : , :  |
| 415 | instantiation | 626 | ⊢  |
| | : , :  |
| 416 | instantiation | 684, 679, 446 | ⊢  |
| | : , : , :  |
| 417 | instantiation | 684, 679, 447 | ⊢  |
| | : , : , :  |
| 418 | instantiation | 462, 448 | ⊢  |
| | : , :  |
| 419 | instantiation | 611, 612, 686, 674, 614, 449, 646, 577, 527 | ⊢  |
| | : , : , : , : , : , :  |
| 420 | instantiation | 617, 450 | ⊢  |
| | : , : , :  |
| 421 | instantiation | 524, 527 | ⊢  |
| | :  |
| 422 | conjecture | | ⊢  |
| | proveit.numbers.numerals.decimals.nat4 |
| 423 | instantiation | 451 | ⊢  |
| | : , : , : , :  |
| 424 | instantiation | 626 | ⊢  |
| | : , :  |
| 425 | theorem | | ⊢  |
| | proveit.physics.quantum.algebra.num_ket_eq |
| 426 | instantiation | 462, 452 | , ⊢  |
| | : , :  |
| 427 | instantiation | 545, 453, 454 | ⊢  |
| | : , : , :  |
| 428 | theorem | | ⊢  |
| | proveit.logic.equality.sub_left_side_into |
| 429 | instantiation | 455, 456, 459, 457 | , ⊢  |
| | : , : , : , :  |
| 430 | instantiation | 458, 459, 674, 612, 614, 487, 488, 490, 491 | , ⊢  |
| | : , : , : , : , : , : , : , : , : , :  |
| 431 | instantiation | 460, 620, 646, 589 | ⊢  |
| | : , :  |
| 432 | instantiation | 617, 461 | ⊢  |
| | : , : , :  |
| 433 | instantiation | 462, 463 | ⊢  |
| | : , :  |
| 434 | conjecture | | ⊢  |
| | proveit.numbers.number_sets.complex_numbers.nonzero_complex_is_complex_nonzero |
| 435 | instantiation | 464, 467, 471, 540, 468, 472, 520*, 523* | ⊢  |
| | : , : , :  |
| 436 | instantiation | 576, 674, 686, 612, 465, 614, 615, 521, 525 | ⊢  |
| | : , : , : , : , : , :  |
| 437 | instantiation | 593, 612, 686, 614, 465, 521, 525 | ⊢  |
| | : , : , : , :  |
| 438 | instantiation | 617, 466 | ⊢  |
| | : , : , :  |
| 439 | instantiation | 588, 615, 467, 468, 469* | ⊢  |
| | : , :  |
| 440 | instantiation | 617, 470 | ⊢  |
| | : , : , :  |
| 441 | instantiation | 588, 615, 471, 472, 473* | ⊢  |
| | : , :  |
| 442 | instantiation | 684, 670, 474 | ⊢  |
| | : , : , :  |
| 443 | instantiation | 581, 475, 583 | , ⊢  |
| | : , :  |
| 444 | instantiation | 576, 612, 686, 674, 614, 476, 582, 507, 583 | , ⊢  |
| | : , : , : , : , : , :  |
| 445 | instantiation | 570 | ⊢  |
| | : , : , :  |
| 446 | instantiation | 477, 680, 651 | ⊢  |
| | : , :  |
| 447 | instantiation | 664, 651 | ⊢  |
| | :  |
| 448 | instantiation | 478, 527 | ⊢  |
| | :  |
| 449 | instantiation | 626 | ⊢  |
| | : , :  |
| 450 | instantiation | 479, 615, 646, 480 | ⊢  |
| | : , : , :  |
| 451 | conjecture | | ⊢  |
| | proveit.numbers.numerals.decimals.tuple_len_4_typical_eq |
| 452 | instantiation | 494, 568, 527 | , ⊢  |
| | : , :  |
| 453 | instantiation | 581, 548, 481 | ⊢  |
| | : , :  |
| 454 | instantiation | 603, 482, 483 | ⊢  |
| | : , : , :  |
| 455 | conjecture | | ⊢  |
| | proveit.linear_algebra.scalar_multiplication.scalar_mult_closure |
| 456 | instantiation | 484, 683, 486, 487, 488 | ⊢  |
| | : , : , :  |
| 457 | instantiation | 485, 683, 486, 487, 488, 489, 490, 491 | , ⊢  |
| | : , : , : , :  |
| 458 | conjecture | | ⊢  |
| | proveit.linear_algebra.tensors.factor_scalar_from_tensor_prod |
| 459 | instantiation | 542, 492, 493 | , ⊢  |
| | : , :  |
| 460 | conjecture | | ⊢  |
| | proveit.numbers.division.div_complex_closure |
| 461 | instantiation | 494, 573, 629 | ⊢  |
| | : , :  |
| 462 | theorem | | ⊢  |
| | proveit.logic.equality.equals_reversal |
| 463 | instantiation | 495, 646, 496, 497 | ⊢  |
| | : , : , :  |
| 464 | conjecture | | ⊢  |
| | proveit.numbers.exponentiation.real_power_of_product |
| 465 | instantiation | 626 | ⊢  |
| | : , :  |
| 466 | instantiation | 617, 498 | ⊢  |
| | : , : , :  |
| 467 | instantiation | 499, 646 | ⊢  |
| | :  |
| 468 | instantiation | 503, 656, 500 | ⊢  |
| | : , :  |
| 469 | instantiation | 603, 501, 502 | ⊢  |
| | : , : , :  |
| 470 | instantiation | 617, 572 | ⊢  |
| | : , : , :  |
| 471 | instantiation | 542, 646, 573 | ⊢  |
| | : , :  |
| 472 | instantiation | 503, 656, 504 | ⊢  |
| | : , :  |
| 473 | instantiation | 603, 505, 506 | ⊢  |
| | : , : , :  |
| 474 | instantiation | 684, 679, 636 | ⊢  |
| | : , : , :  |
| 475 | instantiation | 581, 582, 507 | , ⊢  |
| | : , :  |
| 476 | instantiation | 626 | ⊢  |
| | : , :  |
| 477 | conjecture | | ⊢  |
| | proveit.numbers.multiplication.mult_int_closure_bin |
| 478 | conjecture | | ⊢  |
| | proveit.numbers.negation.mult_neg_one_left |
| 479 | conjecture | | ⊢  |
| | proveit.numbers.addition.subtraction.subtract_from_add |
| 480 | conjecture | | ⊢  |
| | proveit.numbers.numerals.decimals.add_1_1 |
| 481 | instantiation | 545, 508, 509 | ⊢  |
| | : , : , :  |
| 482 | instantiation | 576, 674, 549, 612, 510, 614, 548, 582, 583, 527 | ⊢  |
| | : , : , : , : , : , :  |
| 483 | instantiation | 576, 612, 686, 549, 614, 550, 510, 646, 569, 582, 583, 527 | ⊢  |
| | : , : , : , : , : , :  |
| 484 | conjecture | | ⊢  |
| | proveit.linear_algebra.tensors.tensor_prod_of_vec_spaces_is_vec_space |
| 485 | conjecture | | ⊢  |
| | proveit.linear_algebra.tensors.tensor_prod_is_in_tensor_prod_space |
| 486 | instantiation | 626 | ⊢  |
| | : , :  |
| 487 | instantiation | 511, 683 | ⊢  |
| | :  |
| 488 | instantiation | 511, 512 | ⊢  |
| | :  |
| 489 | instantiation | 626 | ⊢  |
| | : , :  |
| 490 | conjecture | | ⊢  |
| | proveit.physics.quantum.algebra.ket_one_in_qubit_space |
| 491 | instantiation | 513, 673, 624 | , ⊢  |
| | : , :  |
| 492 | instantiation | 684, 657, 514 | ⊢  |
| | : , : , :  |
| 493 | instantiation | 545, 515, 516 | , ⊢  |
| | : , : , :  |
| 494 | conjecture | | ⊢  |
| | proveit.numbers.addition.commutation |
| 495 | conjecture | | ⊢  |
| | proveit.numbers.exponentiation.product_of_pos_powers |
| 496 | instantiation | 684, 517, 667 | ⊢  |
| | : , : , :  |
| 497 | instantiation | 684, 517, 621 | ⊢  |
| | : , : , :  |
| 498 | instantiation | 603, 518, 519 | ⊢  |
| | : , : , :  |
| 499 | conjecture | | ⊢  |
| | proveit.numbers.exponentiation.sqrt_complex_closure |
| 500 | instantiation | 684, 522, 667 | ⊢  |
| | : , : , :  |
| 501 | instantiation | 617, 520 | ⊢  |
| | : , : , :  |
| 502 | instantiation | 524, 521 | ⊢  |
| | :  |
| 503 | conjecture | | ⊢  |
| | proveit.numbers.exponentiation.exp_rational_non_zero__not_zero |
| 504 | instantiation | 684, 522, 621 | ⊢  |
| | : , : , :  |
| 505 | instantiation | 617, 523 | ⊢  |
| | : , : , :  |
| 506 | instantiation | 524, 525 | ⊢  |
| | :  |
| 507 | instantiation | 542, 646, 526 | , ⊢  |
| | : , :  |
| 508 | instantiation | 581, 566, 527 | ⊢  |
| | : , :  |
| 509 | instantiation | 576, 612, 686, 674, 614, 567, 582, 583, 527 | ⊢  |
| | : , : , : , : , : , :  |
| 510 | instantiation | 570 | ⊢  |
| | : , : , :  |
| 511 | conjecture | | ⊢  |
| | proveit.linear_algebra.complex_vec_set_is_vec_space |
| 512 | instantiation | 528, 686, 663 | ⊢  |
| | : , :  |
| 513 | conjecture | | ⊢  |
| | proveit.physics.quantum.algebra.num_ket_in_register_space |
| 514 | instantiation | 684, 598, 529 | ⊢  |
| | : , : , :  |
| 515 | instantiation | 581, 548, 530 | , ⊢  |
| | : , :  |
| 516 | instantiation | 603, 531, 532 | , ⊢  |
| | : , : , :  |
| 517 | conjecture | | ⊢  |
| | proveit.numbers.number_sets.real_numbers.rational_pos_within_real_pos |
| 518 | instantiation | 603, 533, 534 | ⊢  |
| | : , : , :  |
| 519 | instantiation | 603, 535, 536 | ⊢  |
| | : , : , :  |
| 520 | instantiation | 539, 646, 642, 540, 589, 537* | ⊢  |
| | : , : , :  |
| 521 | instantiation | 542, 646, 538 | ⊢  |
| | : , :  |
| 522 | conjecture | | ⊢  |
| | proveit.numbers.number_sets.rational_numbers.rational_pos_within_rational_nonzero |
| 523 | instantiation | 539, 646, 591, 540, 589, 541* | ⊢  |
| | : , : , :  |
| 524 | conjecture | | ⊢  |
| | proveit.numbers.multiplication.elim_one_left |
| 525 | instantiation | 542, 646, 556 | ⊢  |
| | : , :  |
| 526 | instantiation | 592, 543 | , ⊢  |
| | :  |
| 527 | instantiation | 684, 657, 544 | ⊢  |
| | : , : , :  |
| 528 | conjecture | | ⊢  |
| | proveit.numbers.exponentiation.exp_natpos_closure |
| 529 | conjecture | | ⊢  |
| | proveit.numbers.number_sets.real_numbers.e_is_real_pos |
| 530 | instantiation | 545, 546, 547 | , ⊢  |
| | : , : , :  |
| 531 | instantiation | 576, 674, 549, 612, 551, 614, 548, 582, 583, 568 | , ⊢  |
| | : , : , : , : , : , :  |
| 532 | instantiation | 576, 612, 686, 549, 614, 550, 551, 646, 569, 582, 583, 568 | , ⊢  |
| | : , : , : , : , : , :  |
| 533 | instantiation | 617, 552 | ⊢  |
| | : , : , :  |
| 534 | instantiation | 617, 553 | ⊢  |
| | : , : , :  |
| 535 | instantiation | 554, 612, 686, 674, 614, 555, 573, 629, 556 | ⊢  |
| | : , : , : , : , : , :  |
| 536 | instantiation | 557, 573, 629, 558 | ⊢  |
| | : , : , :  |
| 537 | instantiation | 559, 629, 615, 616* | ⊢  |
| | : , :  |
| 538 | instantiation | 684, 657, 560 | ⊢  |
| | : , : , :  |
| 539 | conjecture | | ⊢  |
| | proveit.numbers.exponentiation.real_power_of_real_power |
| 540 | instantiation | 684, 670, 561 | ⊢  |
| | : , : , :  |
| 541 | instantiation | 603, 562, 563 | ⊢  |
| | : , : , :  |
| 542 | conjecture | | ⊢  |
| | proveit.numbers.exponentiation.exp_complex_closure |
| 543 | instantiation | 684, 657, 564 | , ⊢  |
| | : , : , :  |
| 544 | instantiation | 684, 670, 565 | ⊢  |
| | : , : , :  |
| 545 | theorem | | ⊢  |
| | proveit.logic.equality.sub_right_side_into |
| 546 | instantiation | 581, 566, 568 | , ⊢  |
| | : , :  |
| 547 | instantiation | 576, 612, 686, 674, 614, 567, 582, 583, 568 | , ⊢  |
| | : , : , : , : , : , :  |
| 548 | instantiation | 581, 646, 569 | ⊢  |
| | : , :  |
| 549 | conjecture | | ⊢  |
| | proveit.numbers.numerals.decimals.nat3 |
| 550 | instantiation | 626 | ⊢  |
| | : , :  |
| 551 | instantiation | 570 | ⊢  |
| | : , : , :  |
| 552 | instantiation | 588, 610, 646, 589, 571* | ⊢  |
| | : , :  |
| 553 | instantiation | 617, 572 | ⊢  |
| | : , : , :  |
| 554 | conjecture | | ⊢  |
| | proveit.numbers.addition.disassociation |
| 555 | instantiation | 626 | ⊢  |
| | : , :  |
| 556 | instantiation | 592, 573 | ⊢  |
| | :  |
| 557 | conjecture | | ⊢  |
| | proveit.numbers.addition.subtraction.add_cancel_triple_13 |
| 558 | instantiation | 574 | ⊢  |
| | :  |
| 559 | conjecture | | ⊢  |
| | proveit.numbers.negation.pos_times_neg |
| 560 | instantiation | 575, 642 | ⊢  |
| | :  |
| 561 | instantiation | 684, 679, 652 | ⊢  |
| | : , : , :  |
| 562 | instantiation | 576, 612, 686, 674, 614, 594, 629, 620, 577 | ⊢  |
| | : , : , : , : , : , :  |
| 563 | instantiation | 578, 686, 612, 594, 614, 629, 620, 615, 579* | ⊢  |
| | : , : , : , : , :  |
| 564 | instantiation | 684, 670, 580 | , ⊢  |
| | : , : , :  |
| 565 | instantiation | 684, 679, 651 | ⊢  |
| | : , : , :  |
| 566 | instantiation | 581, 582, 583 | ⊢  |
| | : , :  |
| 567 | instantiation | 626 | ⊢  |
| | : , :  |
| 568 | instantiation | 684, 657, 584 | , ⊢  |
| | : , : , :  |
| 569 | instantiation | 684, 657, 585 | ⊢  |
| | : , : , :  |
| 570 | conjecture | | ⊢  |
| | proveit.numbers.numerals.decimals.tuple_len_3_typical_eq |
| 571 | instantiation | 603, 586, 587 | ⊢  |
| | : , : , :  |
| 572 | instantiation | 588, 620, 646, 589, 590* | ⊢  |
| | : , :  |
| 573 | instantiation | 684, 657, 591 | ⊢  |
| | : , : , :  |
| 574 | axiom | | ⊢  |
| | proveit.logic.equality.equals_reflexivity |
| 575 | conjecture | | ⊢  |
| | proveit.numbers.negation.real_closure |
| 576 | conjecture | | ⊢  |
| | proveit.numbers.multiplication.disassociation |
| 577 | instantiation | 592, 615 | ⊢  |
| | :  |
| 578 | conjecture | | ⊢  |
| | proveit.numbers.multiplication.mult_neg_any |
| 579 | instantiation | 593, 686, 612, 594, 614, 629, 620 | ⊢  |
| | : , : , : , :  |
| 580 | instantiation | 684, 679, 595 | , ⊢  |
| | : , : , :  |
| 581 | conjecture | | ⊢  |
| | proveit.numbers.multiplication.mult_complex_closure_bin |
| 582 | conjecture | | ⊢  |
| | proveit.numbers.number_sets.complex_numbers.i_is_complex |
| 583 | instantiation | 684, 657, 596 | ⊢  |
| | : , : , :  |
| 584 | instantiation | 684, 670, 597 | , ⊢  |
| | : , : , :  |
| 585 | instantiation | 684, 598, 599 | ⊢  |
| | : , : , :  |
| 586 | instantiation | 617, 618 | ⊢  |
| | : , : , :  |
| 587 | instantiation | 603, 600, 601 | ⊢  |
| | : , : , :  |
| 588 | conjecture | | ⊢  |
| | proveit.numbers.division.div_as_mult |
| 589 | instantiation | 602, 683 | ⊢  |
| | :  |
| 590 | instantiation | 603, 604, 605 | ⊢  |
| | : , : , :  |
| 591 | instantiation | 684, 670, 606 | ⊢  |
| | : , : , :  |
| 592 | conjecture | | ⊢  |
| | proveit.numbers.negation.complex_closure |
| 593 | conjecture | | ⊢  |
| | proveit.numbers.multiplication.elim_one_any |
| 594 | instantiation | 626 | ⊢  |
| | : , :  |
| 595 | instantiation | 684, 607, 608 | , ⊢  |
| | : , : , :  |
| 596 | conjecture | | ⊢  |
| | proveit.physics.quantum.QPE._phase_is_real |
| 597 | instantiation | 684, 679, 609 | , ⊢  |
| | : , : , :  |
| 598 | conjecture | | ⊢  |
| | proveit.numbers.number_sets.real_numbers.real_pos_within_real |
| 599 | conjecture | | ⊢  |
| | proveit.numbers.number_sets.real_numbers.pi_is_real_pos |
| 600 | instantiation | 619, 610, 629 | ⊢  |
| | : , :  |
| 601 | instantiation | 611, 674, 686, 612, 613, 614, 629, 620, 615, 616* | ⊢  |
| | : , : , : , : , : , :  |
| 602 | conjecture | | ⊢  |
| | proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos |
| 603 | axiom | | ⊢  |
| | proveit.logic.equality.equals_transitivity |
| 604 | instantiation | 617, 618 | ⊢  |
| | : , : , :  |
| 605 | instantiation | 619, 620, 629 | ⊢  |
| | : , :  |
| 606 | instantiation | 684, 666, 621 | ⊢  |
| | : , : , :  |
| 607 | instantiation | 637, 622, 638 | ⊢  |
| | : , :  |
| 608 | assumption | | ⊢  |
| 609 | instantiation | 684, 623, 624 | , ⊢  |
| | : , : , :  |
| 610 | instantiation | 684, 657, 625 | ⊢  |
| | : , : , :  |
| 611 | conjecture | | ⊢  |
| | proveit.numbers.multiplication.distribute_through_sum |
| 612 | axiom | | ⊢  |
| | proveit.numbers.number_sets.natural_numbers.zero_in_nats |
| 613 | instantiation | 626 | ⊢  |
| | : , :  |
| 614 | conjecture | | ⊢  |
| | proveit.core_expr_types.tuples.tuple_len_0_typical_eq |
| 615 | instantiation | 684, 657, 627 | ⊢  |
| | : , : , :  |
| 616 | instantiation | 628, 629 | ⊢  |
| | :  |
| 617 | axiom | | ⊢  |
| | proveit.logic.equality.substitution |
| 618 | instantiation | 630, 631, 681, 632* | ⊢  |
| | : , :  |
| 619 | conjecture | | ⊢  |
| | proveit.numbers.multiplication.commutation |
| 620 | instantiation | 684, 657, 633 | ⊢  |
| | : , : , :  |
| 621 | instantiation | 634, 667, 635 | ⊢  |
| | : , :  |
| 622 | instantiation | 650, 636, 665 | ⊢  |
| | : , :  |
| 623 | instantiation | 637, 638, 639 | ⊢  |
| | : , :  |
| 624 | assumption | | ⊢  |
| 625 | instantiation | 647, 648, 640 | ⊢  |
| | : , : , :  |
| 626 | conjecture | | ⊢  |
| | proveit.numbers.numerals.decimals.tuple_len_2_typical_eq |
| 627 | instantiation | 684, 670, 641 | ⊢  |
| | : , : , :  |
| 628 | conjecture | | ⊢  |
| | proveit.numbers.multiplication.elim_one_right |
| 629 | instantiation | 684, 657, 642 | ⊢  |
| | : , : , :  |
| 630 | conjecture | | ⊢  |
| | proveit.numbers.exponentiation.neg_power_as_div |
| 631 | instantiation | 684, 643, 644 | ⊢  |
| | : , : , :  |
| 632 | instantiation | 645, 646 | ⊢  |
| | :  |
| 633 | instantiation | 647, 648, 673 | ⊢  |
| | : , : , :  |
| 634 | conjecture | | ⊢  |
| | proveit.numbers.multiplication.mult_rational_pos_closure_bin |
| 635 | instantiation | 684, 682, 673 | ⊢  |
| | : , : , :  |
| 636 | instantiation | 664, 649 | ⊢  |
| | :  |
| 637 | conjecture | | ⊢  |
| | proveit.numbers.number_sets.integers.int_interval_within_int |
| 638 | conjecture | | ⊢  |
| | proveit.numbers.number_sets.integers.zero_is_int |
| 639 | instantiation | 650, 651, 652 | ⊢  |
| | : , :  |
| 640 | instantiation | 653, 673, 681 | ⊢  |
| | : , :  |
| 641 | instantiation | 684, 679, 665 | ⊢  |
| | : , : , :  |
| 642 | instantiation | 684, 670, 654 | ⊢  |
| | : , : , :  |
| 643 | conjecture | | ⊢  |
| | proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero |
| 644 | instantiation | 684, 655, 656 | ⊢  |
| | : , : , :  |
| 645 | conjecture | | ⊢  |
| | proveit.numbers.exponentiation.complex_x_to_first_power_is_x |
| 646 | instantiation | 684, 657, 658 | ⊢  |
| | : , : , :  |
| 647 | theorem | | ⊢  |
| | proveit.logic.sets.inclusion.unfold_subset_eq |
| 648 | instantiation | 659, 660 | ⊢  |
| | : , :  |
| 649 | instantiation | 684, 661, 673 | ⊢  |
| | : , : , :  |
| 650 | conjecture | | ⊢  |
| | proveit.numbers.addition.add_int_closure_bin |
| 651 | instantiation | 662, 680, 663 | ⊢  |
| | : , :  |
| 652 | instantiation | 664, 665 | ⊢  |
| | :  |
| 653 | conjecture | | ⊢  |
| | proveit.numbers.addition.add_nat_pos_closure_bin |
| 654 | instantiation | 684, 666, 667 | ⊢  |
| | : , : , :  |
| 655 | conjecture | | ⊢  |
| | proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero |
| 656 | instantiation | 684, 668, 669 | ⊢  |
| | : , : , :  |
| 657 | conjecture | | ⊢  |
| | proveit.numbers.number_sets.complex_numbers.real_within_complex |
| 658 | instantiation | 684, 670, 671 | ⊢  |
| | : , : , :  |
| 659 | theorem | | ⊢  |
| | proveit.logic.sets.inclusion.relax_proper_subset |
| 660 | conjecture | | ⊢  |
| | proveit.numbers.number_sets.real_numbers.nat_pos_within_real |
| 661 | conjecture | | ⊢  |
| | proveit.numbers.number_sets.integers.nat_pos_within_int |
| 662 | conjecture | | ⊢  |
| | proveit.numbers.exponentiation.exp_int_closure |
| 663 | instantiation | 684, 672, 673 | ⊢  |
| | : , : , :  |
| 664 | conjecture | | ⊢  |
| | proveit.numbers.negation.int_closure |
| 665 | instantiation | 684, 685, 674 | ⊢  |
| | : , : , :  |
| 666 | conjecture | | ⊢  |
| | proveit.numbers.number_sets.rational_numbers.rational_pos_within_rational |
| 667 | instantiation | 675, 676, 677 | ⊢  |
| | : , :  |
| 668 | conjecture | | ⊢  |
| | proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero |
| 669 | instantiation | 684, 678, 683 | ⊢  |
| | : , : , :  |
| 670 | conjecture | | ⊢  |
| | proveit.numbers.number_sets.real_numbers.rational_within_real |
| 671 | instantiation | 684, 679, 680 | ⊢  |
| | : , : , :  |
| 672 | conjecture | | ⊢  |
| | proveit.numbers.number_sets.natural_numbers.nat_pos_within_nat |
| 673 | assumption | | ⊢  |
| 674 | theorem | | ⊢  |
| | proveit.numbers.numerals.decimals.nat1 |
| 675 | conjecture | | ⊢  |
| | proveit.numbers.division.div_rational_pos_closure |
| 676 | instantiation | 684, 682, 681 | ⊢  |
| | : , : , :  |
| 677 | instantiation | 684, 682, 683 | ⊢  |
| | : , : , :  |
| 678 | conjecture | | ⊢  |
| | proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int |
| 679 | conjecture | | ⊢  |
| | proveit.numbers.number_sets.rational_numbers.int_within_rational |
| 680 | instantiation | 684, 685, 686 | ⊢  |
| | : , : , :  |
| 681 | conjecture | | ⊢  |
| | proveit.numbers.numerals.decimals.posnat1 |
| 682 | conjecture | | ⊢  |
| | proveit.numbers.number_sets.rational_numbers.nat_pos_within_rational_pos |
| 683 | conjecture | | ⊢  |
| | proveit.numbers.numerals.decimals.posnat2 |
| 684 | theorem | | ⊢  |
| | proveit.logic.sets.inclusion.superset_membership_from_proper_subset |
| 685 | conjecture | | ⊢  |
| | proveit.numbers.number_sets.integers.nat_within_int |
| 686 | conjecture | | ⊢  |
| | proveit.numbers.numerals.decimals.nat2 |
| *equality replacement requirements |